Since this is a very young bird, you should be able to tame her. It will take a lot of time & patience because lovebirds are probably the most difficult to tame if they are parent raised, but it can be done. Since she is already letting you hold her without biting, you've already come a long way. Those lovebird bites can be painful. My suggestion would be to just keep doing what you are doing - spending time with her - holding her - offering treats from your hand - talking to her and possibly to consider clicker training -
Clicker Train Your Bird. Good luck & have fun with your bird.